Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math 
n = int(input())
def isTriangular(n):
    c = 0
    x = (8*n + 1)
    if math.sqrt(x) == int(math.sqrt(x)):
        c=1
    return c
ans = 0
z = n//2
t = 1
i = 1
while i <= z:
    if isTriangular(n-i) == 1 and isTriangular(i) == 1:  
            ans = 1
            print('YES')
            break
    t += 1
    i += t    
if ans == 0:
    print('NO')